Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's...

We show that the dramatically increasing share of income going to top earners is consistent with the rise of the "power law economy" and argue this may reflect networks and increased digitization. Specifically, tax data (1960-2008) show an increasing dispersion of incomes in the portion of the distribution drawn from a power law, as opposed to the long-established log-normal distribution. We pr...

We consider a generalized copy model of the web graph and related networks, and analyze its limiting behaviour. The model is motivated by previously proposed copying models of the web graph, where new nodes copy the link structure of existing nodes, and a certain number of additional random links are introduced. Our model parametrizes the number of random links, thereby allowing for the analysi...

The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local events, the addition of new nodes intracommunity and new links intraor inter-community. Employing growth and preferential attachment mechanisms, we generate the network with a generalized power-law distribution of nodes’ degrees. Furthermore...

in this study, the spatial distribution of overwintered adults of sunn pest, eurygaster integriceps puton, was investigated by using dispersion parameters and indices, mathematical distribution, and regression techniques in rainfed wheat fields by sample size of 1 m2 in 2009 and 2010. the dispersion parameters including: mean-variance test and clumping parameter () showed that the overwintered ...

We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power −α, for some α ∈ (0, 1). Through a rigorous analysis, we show that rank-based attachment models lead to graphs with a p...

We review recent progress in understanding the meaning of mutual information in natural language. Let us define words in a text as strings that occur sufficiently often. In a few previous papers, we have shown that a power-law distribution for so defined words (a.k.a. Herdan's law) is obeyed if there is a similar power-law growth of (algorithmic) mutual information between adjacent portions of ...

In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...